Wednesday, October 16, 2013

Light Ties The Knot

An amazing theoretical advancement on a very old and well-established set of equations.

Physicists have found a very interesting solution to the well-known Maxwell Equations, one in which can form light into interesting geometries and knots.

In the late 1980s, a researcher discovered exact solutions of Maxwell’s equations in free space (containing no electric charge) with the odd property that every field line formed a closed loop, and each loop was linked to another. This structure is called a Hopf fibration, which has been found in other places such as liquid-crystal physics (see 3 June 2013 Viewpoint). Kedia et al. now go a step further with their discovery of exact solutions that are both linked and knotted: the field lines are tied around each other inside a torus.

More coverage and explanation on Physics World.

Identified by Hridesh Kedia at the University of Chicago, along with colleagues at the Polish Academy of Sciences in Warsaw and the Spanish National Research Council in Madrid, the new family of solutions to Maxwell's equations have field lines describing all "torus knots" and "links". Torus knots are those knots that can lie on the surface of a torus, whereas a link is a collection of such knots.

One solution involves magnetic-field lines that trace out a familiar "trefoil" knot around a torus that is aligned in the plane perpendicular to the direction of propagation of the light (see figure). As the light propagates, the knot is distorted but retains the topological property of being a trefoil knot. The electric-field lines have the same structure as the magnetic-field lines but are rotated about the propagation axis by an angle that depends upon the knot. Other solutions include cinquefoil knots and linked rings. 

Still plenty of surprises and interesting solutions out of the old equations!


1 comment:

johnduffieldblog said...

You know Zapper, sometimes I feel as if TQFT, and the wave nature of matter, and electron diffraction, and pair production, and annihilation, never happened. You can make an electron and a positron out of light. Annihilate them and you've got light again. And yet people insist that the electron is some kind of mystic point particle. Even though it's quantum field theory, even though in atomic orbitals "electrons exist as standing waves". As if they don't exist as standing waves even when they aren't in an orbital. Standing wave, standing field. Sigh. Sometimes maybe the answer is just too simple.